There's no reason why a dollhouse can't have an ukelele. I was very apprehensive about trying to make this, but as it turned out, it wasn't as hard as I expected it to be. You need some balsa wood, a very accurate cutter and a lot of common sense.
I printed a very small picture of an ukelele and started by gluing it to a piece of thin cardboard I cut in the same shape. I did this because in case I didn't manage to cut out the exact shape of the ukelele out of the balsa wood, I'd still be able to suggest the instrument by gluing the cardboard shape on it. I always think of a plan B because I usually need one to save face.
Next I carefully cut out the "head" of the ukelele. I started by cutting out a rectangle, out of which I cut the details. Be VERY careful, balsa wood splinters, scales off, falls to pieces, explodes, whatever. I glued cylindric little beads to it to make the tuning keys.
The body was what I was most afraid of. But it went ok. You draw the outlines of the uke on a piece of balsa and then with a fine cutter you start shaping it.
When this is done, you glue the picture of the uke onto the body you have just made, you attach the "head" and there, you have a dollhouse ukelele: